# The Excel WEIBULL.DIST Function

Weibull Distribution

The Weibull Distribution is a probability distribution that is frequently used in engineering.

The Weibull probability density function is given by the equation:

where x is the independent variable, α is the shape parameter, and β is the scale parameter.

The Weibull cumulative distribution function is:

The Weibull Distribution is explained in detail on the Wikipedia Weibull Distribution Page

## Function Description

The Excel Weibull.Dist function calculates the Weibull Probability Density Function or the Weibull Cumulative Distribution Function for a supplied set of parameters.

Although the function is new in Excel 2010, it is simply an updated version of the Weibull function, which is available in earlier versions of Excel.

The syntax of the Weibull.Dist function is:

WEIBULL.DIST( x, alpha, beta, cumulative )

Where the function arguments are:

x - The value at which the function is to be calculated (must be ≥ 0).
alpha - The Shape parameter to the distribution (must be > 0).
beta - The Scale parameter to the distribution (must be > 0).
cumulative -

A logical argument which denotes the type of distribution to be used:

 TRUE = Weibull Cumulative Distribution Function FALSE = Weibull Probability Density Function.

## Weibull.Dist Function Examples

### Example 1 - Weibull Probability Density Function

Weibull Probability Density Function with α = 3 and β = 1

The above chart on the right shows the Weibull Probability Density Function with the shape parameter, α = 3 and the scale parameter, β = 1.

If you want to calculate the value of this function at x = 1, this can be done with the Excel Weibull.Dist function, as follows:

=WEIBULL.DIST( 1, 3, 1, FALSE )

This gives the result 1.10363832351433.

### Example 2 - Weibull Cumulative Distribution Function

Weibull Cumulative Distribution Function with α = 5 and β = 1.5

The above chart on the right shows the Weibull Cumulative Distribution Function with the shape parameter, α = 5 and the scale parameter, β = 1.5.

If you want to calculate the value of this function at x = 2, this can be done by using the Weibull.Dist function, as follows:

=WEIBULL.DIST( 2, 5, 1.5, TRUE )

This gives the result 0.985212776817482.

For further details of the Excel Weibull.Dist function, see the Microsoft Office website.

## Weibull.Dist Function Errors

If you get an error from the Excel Weibull.Dist function this is likely to be one of the following:

Common Errors
 #NUM! - Occurs if either: The supplied value of x is < 0   or The supplied alpha or the supplied beta argument is ≤ 0. #VALUE! - Occurs if any of the supplied arguments is non-numeric.